diff --git a/matrix.c b/matrix.c
index 3270845..85f8497 100644
--- a/matrix.c
+++ b/matrix.c
@@ -14,16 +14,17 @@ Matrix createMatrix(unsigned int rows, unsigned int cols)
 
     if (rows > 0 || cols > 0)
     {
-        m.buffer = malloc (rows * cols * sizeof(int));
+        m.buffer = malloc(rows * cols * sizeof(int));
     }
-    
+
     return m;
 }
 
 void clearMatrix(Matrix *matrix)
 {
-    
-    if (matrix == NULL) {
+
+    if (matrix == NULL)
+    {
         return;
     }
 
@@ -38,21 +39,21 @@ void clearMatrix(Matrix *matrix)
 
 void setMatrixAt(MatrixType value, Matrix matrix, unsigned int rowIdx, unsigned int colIdx)
 {
-    matrix.buffer[rowIdx * matrix.cols + colIdx] = value; //setzte Matrix auf den Wert value am Punkt (row col)
+    matrix.buffer[rowIdx * matrix.cols + colIdx] = value; // setzte Matrix auf den Wert value am Punkt (row col)
 }
 
 MatrixType getMatrixAt(const Matrix matrix, unsigned int rowIdx, unsigned int colIdx)
 {
     MatrixType value = 0;
 
-    return value = matrix.buffer[rowIdx * matrix.cols + colIdx]; //hole Wert value am Punkt (row col)
+    return value = matrix.buffer[rowIdx * matrix.cols + colIdx]; // hole Wert value am Punkt (row col)
 }
 
 Matrix add(const Matrix matrix1, const Matrix matrix2)
 {
     Matrix result = {0};
- 
-    if(matrix1.rows != matrix2.rows || matrix1.cols != matrix2.cols)
+
+    if (matrix1.rows != matrix2.rows || matrix1.cols != matrix2.cols)
     {
         return result;
     }
@@ -61,21 +62,20 @@ Matrix add(const Matrix matrix1, const Matrix matrix2)
     result.cols = matrix1.cols;
     result.buffer = malloc(result.rows * result.cols * sizeof(MatrixType));
 
-    //wenn buffer nicht allokiert werden kann dann zurücksetzen und abbrechen
-    if(result.buffer == NULL)
+    // wenn buffer nicht allokiert werden kann dann zurücksetzen und abbrechen
+    if (result.buffer == NULL)
     {
         result.rows = result.cols = 0;
 
         return result;
     }
 
-    //Matritzenaddition
-    for (unsigned int i = 0; i < result.rows; i++) 
+    // Matritzenaddition
+    for (unsigned int i = 0; i < result.rows; i++)
     {
-        for (unsigned int j = 0; j < result.cols; j++) 
+        for (unsigned int j = 0; j < result.cols; j++)
         {
             result.buffer[i * result.cols + j] = matrix1.buffer[i * matrix1.cols + j] + matrix2.buffer[i * matrix2.cols + j];
-            
         }
     }
     return result;
@@ -84,35 +84,38 @@ Matrix add(const Matrix matrix1, const Matrix matrix2)
 Matrix multiply(const Matrix matrix1, const Matrix matrix2)
 {
     Matrix result = {0};
- 
-    if(matrix1.rows != matrix2.rows || matrix1.cols != matrix2.cols)
+
+    if (matrix1.cols != matrix2.rows)
     {
         return result;
     }
 
     result.rows = matrix1.rows;
-    result.cols = matrix1.cols;
+    result.cols = matrix2.cols;
     result.buffer = malloc(result.rows * result.cols * sizeof(MatrixType));
 
-    //wenn buffer nicht allokiert werden kann dann zurücksetzen und abbrechen
-    if(result.buffer == NULL)
+    // wenn buffer nicht allokiert werden kann dann zurücksetzen und abbrechen
+    if (result.buffer == NULL)
     {
         result.rows = result.cols = 0;
 
         return result;
     }
 
-    //Matritzenmultiplikation
-    for (unsigned int i = 0; i < result.rows; i++) 
+    // Matritzenmultiplikation
+    for (int r = 0; r < result.rows; r++) // Zeile in Ergebnis
     {
-        for (unsigned int j = 0; j < result.cols; j++) 
+        for (int m = 0; m < result.cols; m++) // Spalte in Ergebnis
         {
-            MatrixType sum = 0;
-            for (unsigned int k = 0; k < matrix1.cols; k++) 
+            MatrixType sum = 0; 
+
+            for (int n = 0; n < matrix1.cols; n++) 
             {
-                sum += matrix1.buffer[i * matrix1.cols + k] * matrix2.buffer[k * matrix2.cols + j];
+                sum += matrix1.buffer[r * matrix1.cols + n] *
+                       matrix2.buffer[n * matrix2.cols + m];
             }
-            result.buffer[i * result.cols + j] = sum;
+
+            result.buffer[r * result.cols + m] = sum; 
         }
     }